Related papers: Eigenvalues and Eigenvectors of the Staggered Dira…
We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at finite chemical potential, and show that the Dirac…
The finite temperature phase diagram of QCD with two massless quark flavors is not yet understood because of the subtle effects of anomalous $U_A(1)$ symmetry. In this work we address this issue by studying the fate of the anomalous…
We provide eigenvalue asymptotics for a Dirac-type operator on $\mathbb Z^n$, $n\geq 2$, perturbed by multiplication operators that decay as $|\mu|^{-\gamma}$ with $\gamma<n$. We show that the eigenvalues accumulate near the value of the…
Recently, random matrix theory predictions for the distribution of low-lying Dirac operator eigenvalues have been extended to include lattice effects for both staggered and Wilson fermions. We computed low-lying eigenvalues for the…
The operator product expansion of current correlators at short distances, and the notion of QCD-hadron duality are the cornerstone of QCD sum rules. The extension of this programme to $T \neq 0$ is discussed, together with applications to…
We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac…
In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…
We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD_3 at small lattice coupling constant beta has exactly the same shape as in QCD_4. This observation is quite surprising, since universal…
We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields:…
We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an Instanton Liquid Model (ILM) at temperatures around the chiral phase transition. For two massless quark flavors we observe that at the chiral…
In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator and hence as…
We compute by Monte Carlo methods the individual distributions of the $k$th smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge…
Consider the Schr\"{o}dinger operator $H = -\Delta + V$, where the potential $V$ is real, $\mathbb{Z}^2$-periodic, and additionally invariant under the symmetry group of the square. We show that, under typical small linear deformations of…
We study physics at temperatures just above the QCD phase transition (Tc) using chiral (overlap) Fermions in the quenched approximation of lattice QCD. Exact zero modes of the overlap Dirac operator are localized and their frequency of…
The order and the nature of the finite-temperature phase transition of QCD with two flavors of dynamical quarks is investigated. An analysis of the critical exponent of the specific heat is performed through finite-size and finite-mass…
We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the…
We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and…
We probe the SU(3) vacuum using eigenvectors of the Dirac operator with an arbitrary phase for the temporal boundary condition. We consider configurations with topological charge |Q| = 1 near the QCD phase transition and at low temperatures…
The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the…
We consider the spectrum of the staggered Dirac operator with SU(2) gauge fields. Our study is motivated by the fact that the antiunitary symmetries of this operator are different from those of the SU(2) continuum Dirac operator. In this…